基于代理模型的指数型功能梯度板固有频率优化

Frequency optimization of power-law functionally graded plates via surrogate model

针对指数型功能梯度板的固有频率优化问题,提出一种基于代理模型的优化方法。采用一种基于自然邻近插值的无网格数值方法——自然单元法,建立功能梯度板的一阶剪切变形理论的自由振动分析格式。选取样本点,用自然单元法计算相应固有频率,然后基于此建立梯度指数-频率代理模型,采用Nelder-Mead单纯形法优化梯度指数使板的固有频率达到预设值。通过算例验证算法的计算效率和精度。结果表明,基于分段三次Hermite插值构造的代理模型具有较高的精度;基于代理模型的优化结果避免了多次调用自然单元法计算频率,提高了计算效率。

A surrogate based technique to address natural frequency optimization problems of a power-law functionally graded plate was proposed.The natural element method was employed to conduct the direct free vibration analysis based on the first order shear deformation plate theory,which is a kind of meshless method based on the natural neighbor interpolation.Initially,some sample data were selected to construct the gradient index-frequency surrogate model.Later,a nonlinear optimization problem of the fundamental frequency was formulated,and the optimum solution was obtained by using Nelder-Mead simplex method.Several numerical examples were given to validate the efficiency and feasibility of the proposed method.It is observed that the piecewise cubic Hermite interpolating polynomial produces the best surrogate model with few sample data.The surrogate-based method improves the numerical efficiency by eliminating repeated frequency calculations.